This work focuses on the properties and structures of Hom-Lie algebras of generalized \(\mathfrak {sl}(2)\) -type. We construct classes of linear twisting maps that turn a skew-symmetric algebra of generalized \(\mathfrak {sl}(2)\) -type into a Hom-Lie algebra, and identify subclasses that result in multiplicative Hom-Lie algebras. We explore ideals, Hom-ideals, subalgebras, and Hom-subalgebras, emphasizing derived series, central descending series, and nilpotence and solvability properties. We also investigate the invariance of these subalgebras under the linear twisting maps and determine whether these subalgebras are weak subalgebras, Hom-subalgebras, weak ideals, or Hom-ideals. In particular, we examine these subalgebras and properties for the subfamilies of non-multiplicative Hom-Lie algebras of generalized \(\mathfrak {sl}(2)\) -type, highlighting the differences between non-multiplicative and multiplicative cases.